Posted
by
timothyon Thursday September 16, 2010 @06:40PM
from the I'm-a-good-guesser-in-binary-too dept.

gregg writes "A researcher has calculated the 2,000,000,000,000,000th digit of pi — and a few digits either side of it. Nicholas Sze, of technology firm Yahoo, determined that the digit — when expressed in binary — is 0."

Really? You "could care less"? So... that means that you actually do care, right? I mean, since you just said it is possible for you to care less than you do. I'm just sayin'...
Just for your edification, the proper way to say what you are trying to say is, "I could not care less."
And with regard to the subject at hand in this thread, the idea that someone's poor English skills could have any bearing whatsoever on his or her skills at mathematics is just laughable and shows how little anyone presuming su

The attention to detail one pays in one field of endeavor is somewhat of an indicator of how much attention to detail one pays overall. Sure, your defense is the SAT separates the two, but the brain doesn't work on different problem classes completely independently!

There are two ways to express uncaring: "I could not care less", meaning I care as little as possible for this thing, in fact it is not possible for me to care any less than I do right now.

Yeah, that's just fucking terrible. Honestly I'm getting so sick of people writing terrible, terrible blog postings on supposedly high tech blogs. If this were a cat blog, I would understand, but its just silly for slashdot to post such crap. Why does this happen?-Taylor

Regardless of what actually happened, there isn't any computation that requires keeping data in memory rather than hard disk. Memory is just faster, if you need more space for the computation, you can always actually use the 100 disks.

Well 50% chance if your zero is binary or 10% chance if your zero is decimal. Good thing the article let us know;). Or you can't really ask that question if it isn't a value that ever changes, ever. Or maybe you can. Probably.

Off chance (no pun intended) does anybody know if the decimal number distribution for pie breaks out to an equal distribution for numbers 0-9? Because that off-chance might changes things, probably. Crumb size is important.

The interesting thing about this article is how they calculated the digits. They broke the problem up into small pieces and had them calculated in parallel. This approach isn't something that's new or all the unique, but what is is applied to is. Most mathematical calculations are done in a near linear fashion, not in parallel. So for them to be able to do this is a big step forward in how we approach these types of problem in the future.

The interesting thing about this article is how they calculated the digits. They broke the problem up into small pieces and had them calculated in parallel. This approach isn't something that's new or all the unique, but what is is applied to is. Most mathematical calculations are done in a near linear fashion, not in parallel. So for them to be able to do this is a big step forward in how we approach these types of problem in the future.

I've always wondered about these ridiculously precise values of pi - doesn't that imply a measurement (of circumference or diameter) smaller than the Planck length? What's the point of 2 trillion decimals of precision?

Well, the radius of the visible universe is roughly 7.6 * 10^6 Planck lengths [google.com]. That means the volume is on the order of 10^183 cubic Planck lengths. So, if you can calculate PI to 200 digits or so, you're really accurate. At some point, more accurate than spacetime itself.

FYI, this is due to the expansion of the visible universe projected out from what we can see. I.E., we see a galaxy 13 billion light years out moving away from us at near C, and now it is 46 billion light years away.

Just tried this. Calculated the circumference of a circle with a radius of 1 meter using Pi to 7 digits (3.1415926) and using Pi to 100 digits. The discrepancy is around 1.0718 * 10^-7m, or around 107 nanometers. That's quite a small discrepancy, and even many scientific calculators will have a more precise value of Pi. By using 10 digits instead of 7, the discrepancy falls to 1.795 * 10^-10m, taking it into picometer range. Granted, this is not Planck length range, but goes a long way to show that yeah, qu

Pi has the property that all binary strings of a given length occur with equal frequency, making it an excellent source of fair pseudorandom bits. There are plenty of applications in which 2 quadrillion pseudorandom bits is grossly insufficient.

just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.

just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.

Actually finding large primes has very little to do with factorization. In general, the most efficient factorization procedures, the elliptic curve sieve and the general number field sieve http://en.wikipedia.org/wiki/Number_field_sieve [wikipedia.org] don't benefit from knowing any primes in advance beyond a few very small primes. Moreover, the largest primes known are all of special forms that don't show up very often. For example, the very largest primes are known as Mersenne primes which are primes which are 1 less tha

just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.

Actually finding large primes has very little to do with factorization. In general, the most efficient factorization procedures, the elliptic curve sieve and the general number field sieve http://en.wikipedia.org/wiki/Number_field_sieve [wikipedia.org] don't benefit from knowing any primes in advance beyond a few very small primes. Moreover, the largest primes known are all of special forms that don't show up very often. For example, the very largest primes are known as Mersenne primes which are primes which are 1 less than a power of 2. We can determine if such numbers are prime using a very efficient test called the Lucas-Lehmer test. The largest such prime known today is 2^43,112,609-1. This is much, much larger than any number we'd want to practically factor (for example numbers used in RSA encryption are generally on the order of a few hundred digits. It is believed that numbers with 2000 or so digits will be secure for the indefinite future). So yeah, finding large primes is about as useful as this when it comes to practical factoring. There are other somewhat good reasons to be interested in finding large primes, but factoring isn't one of them.

We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.

Parent is correct, digits of pi can be calculated independently in base 2, 4, 8, 16 or 2^n since the 1990s [maa.org]. So, it is possible to calculate the 2,000,000,000,000,000th number of pi without calculating the digits before that one. Now, if we want to calculate the digit in decimal (or converse the binary digit to decimal), we need to calculate all of the two-quadrillion digits. Knowing this digit is in itself not very interesting.